名校
解题方法
1 . 如图直角坐标系中,角
、角
的终边分别交单位圆于A、B两点,若B点的纵坐标为
,且满足
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4efa4012cea784b7b9b570b24612fd37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278a447ca0fd92f34000a233181e15cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744cd8216f2335344934f142f0de9647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967e2cbf86e6c86455d63a159ef284d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9817af6bc1c9edd4d48fe8f203d416e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/6d11b63a-8b83-4935-b61f-054ab2ee1ae4.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-07更新
|
479次组卷
|
13卷引用:【全国市级联考】江西省南昌市2018届高三第二轮复习测试六理科数学试题
【全国市级联考】江西省南昌市2018届高三第二轮复习测试六理科数学试题【全国百强校】河北省衡水中学2019届高三上学期三调考试数学(文)试题【全国百强校】辽宁省沈阳市东北育才学校2019届高三上学期第三次模拟数学(理)试题【全国百强校】山西省平遥中学2019届高三上学期11月质检数学(文)试题(已下线)【全国百强校】河北省衡水中学2019届高三下学期三模试卷数学(理科)试题河北省衡水中学2019-2020学年高三下学期七调数学(理)试题江苏省苏州市八校联盟2020-2021学年高三上学期10月第一次适应性检测数学试题(已下线)第12练 三角函数的概念及诱导公式-2021年高考数学(理)一轮复习小题必刷(已下线)第11练 三角函数的概念及诱导公式-2021年高考数学(文)一轮复习小题必刷河北省衡水中学2021届高三上学期期中数学(文)试题江苏省镇江市扬中市第二高级中学2024届高三上学期期末模拟数学试题(一)(已下线)第18讲 三角恒等变换(练)-2022年高考数学一轮复习讲练测(课标全国版)福建省部分优质高中2023-2024学年高一下学期入学质量抽测数学试卷
解题方法
2 . 对于函数
,
,如果存在实数
,
使得函数
,那么我们称
为函数
,
的“
函数”.
(1)已知
,
,试判断
能否为函数
,
的“
函数”,若是,请求出
,
的值;若不是,说明理由;
(2)已知
,
,
为函数
,
的“
函数“,且
,
,解不等式
;
(3)已知
,
,
为函数
,
的“
函数“(其中
,
,
的定义域为
,当且仅当
时,
取得最小值4.若对任意正实数
,
,且
,不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ed6155f2ed4ff240aa839de87f8a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0ae50d5993a332b5cddb022eaa6f1e.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd5511310051b98188576c0879b8b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eeda0d8d85ca30ce483e2784691ddc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046def789ca5b0f8d6acf15bb55fed4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0ae50d5993a332b5cddb022eaa6f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557eb194cf0abe382609f8e1325b4197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280fdf3bab62f1f7bf22db78375f2eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0ae50d5993a332b5cddb022eaa6f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea998345984b6d1bbffa1e667365ed6.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253893d2bf2b944a6de271463c3e7929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76535a5fa102477fc8621b2f3cc70f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0ae50d5993a332b5cddb022eaa6f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04174f3c9351bc05bcf604d18ab8c44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419504736c4934f6e0df4114c3743944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626382f10e9cd843a36e2c35bc430e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
3 . 在下列选项中,正确的是( )
A.![]() |
B.![]() |
C.存在角![]() ![]() |
D.对于任意角![]() ![]() |
您最近一年使用:0次
解题方法
4 . 设
为直线l上的两点,则
,我们把向量
以及与它平行的向量都称为直线l的方向向量,把与直线l的方向向量垂直的向量称为直线l的法向量.若直线l经过点
,则直线的一个法向量
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a00dc6f0af494437c9f98223f3e861f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632cca92e5aba4d4c20bc4ac202705cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4f9cc2cab37cd7e1d991739627f94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee304d78babb475823d1514f2027406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
5 . 已知
为自然对数的底数,
.
(1)求
的单调区间;
(2)证明
有且仅有两个零点;
(3)问:函数
与
的图象有几条公切线?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6bf7c3198cdd4dafc81e3992f34bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f184f195e983df4014e6c57a2e7ee67.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575df2758d348d7d5b889fb5ad8ddafe.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575df2758d348d7d5b889fb5ad8ddafe.png)
(3)问:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
6 . 如图,有一块边长为200米的正方形地块
,其中曲边三角形
是一个小池塘,点
分别在边界
上,且距离
点都为100米,池塘曲边
是一段抛物线,该抛物线的顶点为
,对称轴为边界
所在直线.现准备在边
和
间分别选择两点
,修建一条观光直线小径
,小径
恰好只经过池塘边
上一个点
(不含端点).绿化部门拟在五边形
区域内栽种花草.记点
到边界
的距离为
米,花草区域
面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/dd80dd2d-e5d4-485b-9cdf-120a1ec52304.png?resizew=140)
(1)求函数
的表达式,并写出函数
的定义域;
(2)求花草区域
面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5898ecbb5c528fa6cd5844d2133eb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a184872da2b77693ee06d32a41fa40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a184872da2b77693ee06d32a41fa40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5451a66fb4f48811e042d8ca250f51.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/dd80dd2d-e5d4-485b-9cdf-120a1ec52304.png?resizew=140)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5451a66fb4f48811e042d8ca250f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5451a66fb4f48811e042d8ca250f51.png)
(2)求花草区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a184872da2b77693ee06d32a41fa40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5451a66fb4f48811e042d8ca250f51.png)
您最近一年使用:0次
解题方法
7 . 已知函数
,其定义域为
.
(1)求
,并判断
的单调性;
(2)将函数
的图象向左平移
个单位后,得函数的
图象,如果
为奇函数,求实数
的值;
(3)已知
,对任意
,记
的最大值为
,当实数
为何值时,
最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bdada86abcde7149185625443eab69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b36f2f93bd1e2a3d6a74922ddfcdea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f32da97596b70fb9eb83bc1543ee11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c386fdfd49b91614d7d997a7e317eccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a90170d7ef5ff6d1d63517c166f7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a90170d7ef5ff6d1d63517c166f7a9.png)
您最近一年使用:0次
8 . 已知
,函数
.
(1)当
时,求函数展开式中含
的一次项系数之和;
(2)当
时,
①求函数
展开式中的常数项;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2e59b4e5bf92bf17a136bb555422ff.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ccb9e8d67d838579455ad9f17560a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8d850abc2f58230047cc3f95b846f9.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e70ec8d04593ad6285cd42505e4444.png)
您最近一年使用:0次
解题方法
9 . 请用二项式定理解决下列问题:
(1)求
除以100的余数?
(2)已知
,请比较
与
的大小,并证明你的结论.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bce704393f7b0081a14c656e54dd95.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ddcb15eb419ed659536e1385b09af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
您最近一年使用:0次
10 . 某市有500名考生参加教师招考,从中随机抽取50名学生,这50名学生的考试分数都在区间
内,将这50名考生的考试有关数据统计成下表,以便制成频率分布直方图.
(1)根据表中数据,分别求
的值;
(2)若成绩不低于80分的考生能参加面试,估计参加招考的500名考生中大约有多少考生能参加面试;
(3)若从表中
和
这两组考生中随机抽取两人,求他们的成绩相差不超过10分的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2ce85312957e29410d1eb6e9659cb8.png)
分组 | 频数 | 频率 |
![]() | 0.08 | |
![]() | 0.12 | |
![]() | ![]() | |
![]() | 16 | ![]() |
![]() | 0.16 | |
![]() | ![]() | 0.04 |
合计 | 50 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(2)若成绩不低于80分的考生能参加面试,估计参加招考的500名考生中大约有多少考生能参加面试;
(3)若从表中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1720e1256b8eb4fa308d77814edaf197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a86a6ccc6968f95c9e26db5c4b80d.png)
您最近一年使用:0次